Hello, here is a pentagon ABCDE and

angle ABC=angle BCD=CDE

Calculate giving a reason for each answer the magnitudes of angles (i) ABC and (ii) CDX.

Here is my attempt, for angle ABC, I know the angles in a pentagon add up to 540 degrees, and I know it can be consisting of three separate triangles.

Since the three angles listed are equal, then clearly the line AD which makes the first

triangle AED, bisects angle CDE which clearly means each bisector forming a triangle will give you half of the angle bisected.

So I thought, if I draw a line from B to D, the triangle BDC that would be formed would be all equal angles as all the angles would be bisected, so by that logic angle ABC would be 180/3 = 60.

pentagon.jpg
If there is any other obvious method I'm missing out please tell me any angle rules etc.

AS for angle CDX I'm a bit unsure.

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